We've had two foster cats (Jimmy D and Skrootchie) in the past 6 months diagnosed with this condition and Jenni's had a third in her practice - and it's supposed to be rare!
Basically Pillow Foot involves a swelling of more than one of a cats paw pads, usually with a 'mushy' appearance. It's not necessarily uncomfortable for the cat in a mild form but the pad can swell and split or develop ulcers or sores - and then treatment is needed. It usually affects more than one paw and can affect other parts of the body (e.g. Jimmy D's nose is also swollen in addition to his two forepaws).
We've used antibiotics and anti-inflammatories for treatment (successfully with Jimmy D and timewilltell with Skrootchie) though it takes a few months for significant effects.
The disease isn't well understood and some studies have found a link between it and FIV (Jimmy D has FIV and Skrootchie is looking a likely candidate), so it's worth testing for the virus if you come across pillow foot.
As always, take your animal to a vet if you have any worries - don't rely on the internet for diagnosis!!!
There's not much info online about pillow foot but try these links for more details: